A179436 a(n) = (3*n+7)*(3*n+2)/2.

7, 25, 52, 88, 133, 187, 250, 322, 403, 493, 592, 700, 817, 943, 1078, 1222, 1375, 1537, 1708, 1888, 2077, 2275, 2482, 2698, 2923, 3157, 3400, 3652, 3913, 4183, 4462, 4750, 5047, 5353, 5668, 5992, 6325, 6667, 7018, 7378, 7747, 8125, 8512, 8908, 9313, 9727, 10150

Offset: 0

Author

Paul Curtz, Jan 12 2011

Keywords

• nonn
• easy

Comments

Trisection of A055998.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Leo Tavares, Illustration: Triangulated Triangles.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217, A016777, A016789, A055998, A133694, A153466.

Programs

Magma

[(3*n+7)*(3*n+2)/2: n in [0..50]]; // Vincenzo Librandi, Aug 04 2011

Maple

A179436:=n->(3*n+7)*(3*n+2)/2: seq(A179436(n), n=0..100); # Wesley Ivan Hurt, Apr 24 2017

Mathematica

a[n_] := (3*n + 7)*(3*n + 2)/2; Array[a, 50, 0] (* Amiram Eldar, Mar 27 2022 *)

PARI

a(n)=(3*n+7)*(3*n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: (-7-4*x+2*x^2)/(x-1)^3.

a(n) = a(n-1) + 9*(n+1) = (14 + 27*n + 9*n^2)/2.

a(n) = 2*a(n-1) - a(n-2) + 9.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

a(n) mod 9 = A153466(n) mod 9 = 7.

Sum_{n>=0} 1/a(n) = 1/2-2*Pi*sqrt(3)/45 = 0.2581600... - R. J. Mathar, Apr 07 2011

a(n) = A133694(n+1) + 6*A000217(n+1). - Leo Tavares, Mar 24 2022

Sum_{n>=0} (-1)^n/a(n) = 3/10 - 4*log(2)/15. - Amiram Eldar, Mar 27 2022

From Elmo R. Oliveira, Oct 30 2024: (Start)

E.g.f.: exp(x)*(7 + 18*x + 9*x^2/2).

a(n) = A016777(n+2)*A016789(n)/2. (End)